This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
a) The diagram shows a pentagon. The sum of the exterior angles of any convex polygon is 360^. Step 1: Identify the exterior angles from the diagram. The exterior angles are x, 2x, x+30^, 3x, and 50^. Step 2: Set up the equation by summing the exterior angles and equating them to 360^. x + 2x + (x+30^) + 3x + 50^ = 360^ Step 3: Combine like terms. (x+2x+x+3x) + (30^+50^) = 360^ 7x + 80^ = 360^ Step 4: Solve for x. 7x = 360^ - 80^ 7x = 280^ x = (280^)/(7) x = 40^ b) The diagram shows a pentagon. The sum of the exterior angles of any convex polygon is 360^. Step 1: Identify the exterior angles from the diagram. The exterior angles are 70^, 125^, 2x, x+40^, and 135^. Step 2: Set up the equation by summing the exterior angles and equating them to 360^. 70^ + 125^ + 2x + (x+40^) + 135^ = 360^ Step 3: Combine like terms. (2x+x) + (70^+125^+40^+135^) = 360^ 3x + (195^+40^+135^) = 360^ 3x + (235^+135^) = 360^ 3x + 370^ = 360^ Step 4: Solve for x. 3x = 360^ - 370^ 3x = -10^